Modern Birkhäuser Classics

Schrödinger Equations and Diffusion Theory

Authors: Nagasawa, Masao

  • Self-contained and well-organized introduction to the theory of diffusion processes and applications
  • Recommended to researchers and graduate students in probability theory, functional analysis and quantum dynamics
  • Excellent addition to the literature in probability theory​
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eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0560-5
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  • Included format: PDF
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  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-0348-0559-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Schrödinger Equations and Diffusion Theory addresses the question “What is the Schrödinger equation?” in terms of diffusion processes, and shows that the Schrödinger equation and diffusion equations in duality are equivalent. In turn, Schrödinger’s conjecture of 1931 is solved. The theory of diffusion processes for the Schrödinger equation tells us that we must go further into the theory of systems of (infinitely) many interacting quantum (diffusion) particles.

The method of relative entropy and the theory of transformations enable us to construct severely singular diffusion processes which appear to be equivalent to Schrödinger equations.

The theory of large deviations and the propagation of chaos of interacting diffusion particles reveal the statistical mechanical nature of the Schrödinger equation, namely, quantum mechanics.

The text is practically self-contained and requires only an elementary knowledge of probability theory at the graduate level.

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This book is a self-contained, very well-organized monograph recommended to researchers and graduate students in the field of probability theory, functional analysis and quantum dynamics. (...) what is written in this book may be regarded as an introduction to the theory of diffusion processes and applications written with the physicists in mind. Interesting topics present themselves as the chapters proceed. (...) this book is an excellent addition to the literature of mathematical sciences with a flavour different from an ordinary textbook in probability theory because of the author’s great contributions in this direction. Readers will certainly enjoy the topics and appreciate the  profound mathematical properties of diffusion processes.
(Mathematical Reviews)

About the authors

Masao Nagasawa is professor of mathematics at the University of Zurich, Switzerland.

Table of contents (12 chapters)

  • Introduction and Motivation

    Nagasawa, Masao

    Pages 1-12

  • Diffusion Processes and their Transformations

    Nagasawa, Masao

    Pages 13-54

  • Duality and Time Reversal of Diffusion Processes

    Nagasawa, Masao

    Pages 55-88

  • Equivalence of Diffusion and Schrödinger Equations

    Nagasawa, Masao

    Pages 89-114

  • Variational Principle

    Nagasawa, Masao

    Pages 115-138

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0560-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA
  • ISBN 978-3-0348-0559-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Schrödinger Equations and Diffusion Theory
Authors
Series Title
Modern Birkhäuser Classics
Copyright
1993
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0560-5
DOI
10.1007/978-3-0348-0560-5
Softcover ISBN
978-3-0348-0559-9
Series ISSN
2197-1803
Edition Number
1
Number of Pages
XII, 319
Additional Information
Originally published as volume 86 in the Monographs in Mathematics series
Topics